Conceptually you're wanting to have a new type, so create a new Type that represents the valid values. In your case you want there to only be two possible valid values for your type, so construct those and don't allow any more to be constructed:
public class SomeMeaningfulName
{
private SomeMeaningfulName(string value)
{
Value = value;
}
public string Value { get; }
public static SomeMeaningfulName String1 = new SomeMeaningfulName("First String");
public static SomeMeaningfulName String2 = new SomeMeaningfulName("Second String");
}
Now you can change the type of that property to your new type, and know that it's only one of those two values (for which you can get the string value out of it).